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The perpendicular bisector of the segment joining P(1, 4) and Q(k, 3) cuts the y-axis at -4. Which of the following can be a value of k?

1. 1
2. 2
3. -2
4. -4

Correct answer: -4

Solution

The perpendicular bisector of a segment is a line that is equidistant from both endpoints and intersects the y-axis at the midpoint's y-coordinate. For the segment joining P(1, 4) and Q(k, 3), the midpoint's y-coordinate must equal -4, which occurs when k is -4, making it the only valid option.

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